On the Expressivity of Markov Reward
Abstract
Reward is the driving force for reinforcement-learning agents. This paper is dedicated to understanding the expressivity of reward as a way to capture tasks that we would want an agent to perform. We frame this study around three new abstract notions of “task” that might be desirable: (1) a set of acceptable behaviors, (2) a partial ordering over behaviors, or (3) a partial ordering over trajectories. Our main results prove that while reward can express many of these tasks, there exist instances of each task type that no Markov reward function can capture. We then provide a set of polynomial-time algorithms that construct a Markov reward function that allows an agent to optimize tasks of each of these three types, and correctly determine when no such reward function exists. We conclude with an empirical study that corroborates and illustrates our theoretical findings.
Cite
Text
Abel et al. "On the Expressivity of Markov Reward." Neural Information Processing Systems, 2021.Markdown
[Abel et al. "On the Expressivity of Markov Reward." Neural Information Processing Systems, 2021.](https://mlanthology.org/neurips/2021/abel2021neurips-expressivity/)BibTeX
@inproceedings{abel2021neurips-expressivity,
title = {{On the Expressivity of Markov Reward}},
author = {Abel, David and Dabney, Will and Harutyunyan, Anna and Ho, Mark K and Littman, Michael L. and Precup, Doina and Singh, Satinder P.},
booktitle = {Neural Information Processing Systems},
year = {2021},
url = {https://mlanthology.org/neurips/2021/abel2021neurips-expressivity/}
}